Where numbers enter as parts — and leave as understanding. 52 sessions · 7 units · Ages 7–8
⚙ PLACE VALUE TO 1,000
🔢 REGROUPING
✕ MULTIPLICATION
⅟ FRACTIONS
Our Learning Process
The Factory's 3-Stage Process
🧱
C · Concrete
Touch and move real things — objects at home, on camera. Hands learn first.
→
🖼
P · Pictorial
Draw pictures, diagrams, bar models. Eyes see the pattern.
→
🔢
A · Abstract
Write with numbers and symbols. Brain owns it.
Say: "Grade 2 is the year we move from counting with fingers to thinking with place value. Every big idea today builds on something you already know from Grade 1."
Unit 1 · Sessions 1–8 · Place Value to 1,000
ConcreteSession 2
Hundreds, Tens & Ones
In Grade 1 you worked with Tens & Ones up to 99. Today we add the Hundreds chamber.
H
3
T
4
O
7
Number: 347 | Expanded: 300 + 40 + 7
What each digit is worth
3
= 300 (hundreds)
4
= 40 (tens)
7
= 7 (ones)
Ask: "If I change the hundreds digit to 5, what is the new number? What is its expanded form?"
Unit 1 · Session 4 · Comparing Numbers to 999
Which is greater?
Always compare digit by digit — starting from the left (highest place value first).
H
4
T
2
O
8
428
?
H
3
T
9
O
5
395
4 hundreds > 3 hundreds — so 428 > 395.
Ask: "Why did we only need to look at the hundreds digit here? When would we need to check the tens column too?"
Quick Check · Unit 1 · Session 3
In 563, what is the value of the 5?
H
5
T
6
O
3
Place Value Rule
HUNDREDS digit × 100
TENS digit × 10
ONES digit × 1
Common error: student gives the digit (5) not the place value (500). Ask: "Is the 5 worth 5, or 5 hundreds?"
Unit 2 · Sessions 9–20 · Addition & Subtraction with Regrouping
The Exchange Rule
The Rule
10 →1 ten
10 tens→1 hundred
When any column reaches 10 or more — exchange up. Never say "carry".
Think of it like money: 10 × ₹1 coins = 1 × ₹10 note Same value, different form.
Watch the Exchange — Step by Step
Adding 47 + 35. The ones column gives us 12 — too many for one column. We exchange.
STEP 1 OF 3
ONES
12
→
TENS (after)
8
+
ONES LEFT
2
7 ones + 5 ones = 12 ones. That's too many for the ones column — we need to exchange.
Never say "carry the 1". Say exchange or regroup. The 1 we move to the tens column represents 1 ten — it's the same 10 ones in a new form.
Unit 2 · Session 12 · 2-Digit Addition with Regrouping
Step by Step
Add 47 + 35. Estimate first: ≈80
1
4
7
+
3
5
8
2
Subtraction: same process reversed (Session 15)
62 − 28: can't do 2−8
Exchange 1 ten → 10 ones
Now: 12−8=4, 5−2=3
Answer: 34 ✓
Estimation habit: always ask "about how much?" before calculating. Does our answer make sense?
Quick Check · Unit 2 · Addition with Regrouping
56 + 38 = ?
Estimate first: ≈90
3-Digit Regrouping (Session 13)
247 + 386 = ?
Ones: 7+6=13 → write 3, regroup 1
Tens: 4+8+1=13 → write 3, regroup 1
Hundreds: 2+3+1=6 → write 6
Answer: 633 ✓
The word "exchange" replaces "borrow" and "carry". Nothing disappears — it changes form.
Unit 2 · Session 19 · Multi-Step Word Problems
The Bar Model
A factory makes 246 bolts on Monday and 178 bolts on Tuesday. How many bolts in total?
① WHAT IS ASKED? → Total bolts (Monday + Tuesday)
② ESTIMATE → 250 + 180 ≈ 430
③ BAR MODEL — draw what we know:
Mon: 246
Tue: 178
? (whole — what we're finding)
④ CALCULATE — tap each step:
Ones column → tap
Tens column → tap
Hundreds column → tap
Answer → tap
How to read the bar model
Each bar = one piece of information from the problem.
= a known part
?
= what we're finding
The bar forces you to see: part + part = whole → so we ADD. If the whole and one part are given → we SUBTRACT.
4-Step Protocol
① Read the whole problem
② Draw the bar model
③ Estimate the answer
④ Calculate & check
Ask: "Before you calculate — draw the bar. Which part is the whole? Which parts are given?" If they can draw it, they understand it.
Unit 3 · Sessions 21–28 · Multiplication & Division
Equal Groups → The × Symbol
Concrete — Session 21
3 groups of 4 each:
Group 1
Group 2
Group 3
4+4+4 = 3 × 4 = 12
P · Pictorial — Array (Session 23)
Same 12 objects arranged in rows × columns. Press Rotate ↻ to flip.
3 rows × 4 cols
3×4 = 12 rotate → 4×3 = 12
The total stays 12! This is the commutative property: order doesn't change the product.
Camera task: build the array with objects at home. Count the rows, then rotate your paper 90°. Ask: "Did the total change?" — this visual proof is more powerful than any rule.
Unit 3 · Session 24 · 2× Table
The Doubling Line
Every number that goes in — doubles when it comes out.
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
↓ ⚙ ×2 ⚙ ↓
?
?
?
?
?
?
?
?
?
?
Click each card to reveal.
Flash Drill · 2×
2 × ? = ?
?
Tap to reveal
Pattern: all 2× answers are even. Ask: "What do all the answers end in?"
Unit 3 · Session 25 · 5× Table — Clock Connection
Count the Clock
The 5× table is hidden on every clock — the minute hand counts in 5s.
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60
Pattern: all answers end in 0 or 5 — built-in error checker!
Flash Drill · 5×
5 × ? = ?
?
Tap to reveal
10× Table (Session 25)
Any × 10 → add a 0 7×10=70 · 23×10=230 (Digit moves 1 place left)
Unit 3 · Session 26–27 · Division — Drag & Drop
Share the Bolts
Drag the 12 bolts into 3 workers' bins — share them equally.
BOLT POOL — drag bolts to workers below:
× and ÷ Fact Families (Session 28)
3 × 4 = 12
4 × 3 = 12
12 ÷ 3 = 4
12 ÷ 4 = 3
← Fact family of 3, 4, 12
Two models of division
Sharing: "12 bolts, 3 workers — how many each?" → Divide into equal groups
Grouping: "12 bolts, 4 per box — how many boxes?" → How many groups of 4?
Ask: "If you know 3×4=12, what do you already know about dividing 12? The answer is already there — no new memorising needed."
Unit 4 · Sessions 29–34 · Standard Measurement
Units of Measurement
1 meter
100 cm
Doorknob height ≈ 1m
1 kg
1000 g
Bag of flour ≈ 1kg
1 litre
1000 mL
Water bottle ≈ 1L
1 foot
12 in
Ruler length = 1 ft
1 pound
16 oz
Loaf of bread ≈ 1 lb
1 gallon
4 quarts
Milk jug ≈ 1 gal
Which unit would you use for a pencil?
Metric: Estimate Before Measuring (Session 30)
① Guess: "About how long?"
② Measure with ruler
③ Compare: how close?
Within 20% = good estimate ✓
US: Quick Reference
12 inches = 1 foot
3 feet = 1 yard
16 oz = 1 pound
8 fl oz = 1 cup
4 cups = 1 quart
Camera task: "Find something 10 cm long. Find something about 1 metre. Show me — then estimate: is it closer to 1m or 2m?"
Unit 5 · Session 35 · Time to 5-Minute Intervals
Reading the Clock
In Grade 1 you read o'clock and half-past. Now we read every 5 minutes.
Time: ?
Tap clock to change
What time is it? (AM/PM · Session 36)
Duration · Session 37
Class starts at 3:15, ends at 4:00. How long?
3:15 → 3:30 = 15 min
3:30 → 4:00 = 30 min
Total = 45 minutes ✓
Rule: short hand = hours, long hand = minutes. Identify both hands before reading.
Unit 5 · Sessions 38–39 · Indian Currency & Digital Shop
The Digital Shop
Budget: ₹100
✏️
Pencil
₹12
🧹
Eraser
₹8
📔
Notebook
₹35
📏
Scale
₹20
Cart: empty
Total: ₹0
Change: ₹100
Indian denominations
₹1
₹2
₹5
₹10
₹20
₹50
₹100
Ask: "Three different ways to make ₹50 using our coins and notes." This tests flexible thinking with currency.
Unit 5 · Sessions 40–41 · Tally Marks & Pictographs
Data: Count, Record, Read
Tally Chart — Session 40
Students counted shapes in their room. Each group of 5 = 4 verticals + 1 diagonal cross.
Circles
6
Squares
4
Triangles
3
THE RULE:
4 vertical marks + 1 diagonal = 5. Easy to count in fives.
Pictograph — Session 40
Each ⭐ = 1 shape found
Circles
⭐⭐⭐⭐⭐⭐
Squares
⭐⭐⭐⭐
Triangles
⭐⭐⭐
Data interpretation questions (Session 41) — tap to reveal:
Most common shape? → tap
How many more circles than triangles? → tap
Total shapes? → tap
Camera task: "Survey — count how many of each type of object you see in your room. Draw the tally chart yourself, then transfer it to a pictograph."
Unit 6 · Session 43 · 2D Shape Properties
Sides, Vertices, Curves
We describe shapes by properties — not just names. A shape rotated is the same shape.
Triangle
3 sides · 3 vertices
Square
4 equal sides · 4 vertices
Rectangle
4 sides · 2 pairs equal
Circle
0 sides · 0 vertices · curved
Mystery shape — tap to reveal:
"I have 4 sides and 4 corners. All my sides are equal. What am I?"
3D Shape Properties — Session 44
Cube: 6 faces · 12 edges · 8 vertices
Cuboid: 6 faces · 12 edges · 8 vertices
Sphere: 1 curved face · 0 edges · 0 vertices
Cylinder: 2 flat + 1 curved face
Camera task: find a cube, cuboid, and sphere in your room. Count the faces of each.
Rotate shapes during every session. Ask: "Did the number of sides change when I rotated it? Then it's still the same shape."
Unit 6 · Session 45 · Symmetry Through Paper Folding
Lines of Symmetry
A shape has a line of symmetry if you can fold it and both halves match exactly. Tap each shape to reveal.
Triangle
Tap to reveal
Square
Tap to reveal
Rectangle
Tap to reveal
Circle
Tap to reveal
Paper Fold Lab: fold each shape in half. If both sides match exactly — that's a line of symmetry. Ask: "Can you find another fold that works for the square?"
Unit 6 · Session 46 · Growing Patterns & Rules
Growing Patterns
The rule tells us how the pattern changes each step. Find it, then predict the next term.
Dot Pattern (Sequence: 2, 4, 6, 8…)
Step 1 2
→
Step 2 4
→
Step 3 6
→
?
Step 4
Rule: +2 each step. This is a growing pattern.
2, 4, 6, 8, 10, ... (+2)
5, 10, 15, 20, 25, ... (+5)
1, 4, 7, 10, 13, ... (+3)
What's the rule?
Sequence: 3, 7, 11, 15, ?
Ask: "By how much does it grow each time? Is the rule always the same? That's what makes it a pattern."
Unit 7 · Sessions 48–52 · Fractions — Building on Halves
Unit Fractions: 1/2, 1/3, 1/4
A fraction = equal parts. The denominator tells us how many equal parts in the whole.
WHOLE
1
HALVES — 2 equal parts
1/2
1/2
THIRDS — 3 equal parts
1/3
1/3
1/3
QUARTERS — 4 equal parts
1/4
1/4
1/4
1/4
Why is 1/3 bigger than 1/4? Fewer parts → each part is larger.
Fractions of a Set (Session 50)
1/2 of 8 objects = ?
Paper fold: "Fold a paper in half. Are both sides exactly equal? That equal-ness is what makes it a fraction."
Unit 7 · Session 51 · Comparing Unit Fractions — Fraction Wall
The Fraction Wall
Look at the wall. Which fraction is largest? Which is smallest? Tap to reveal comparisons.
WHOLE
1 whole
HALVES (1/2)
1/2
1/2
THIRDS (1/3)
1/3
1/3
1/3
QUARTERS (1/4)
1/4
1/4
1/4
1/4
Tap: Which is biggest?
Tap: Is 1/4 > 1/2?
Key misconception (Session 51): students think 1/4 > 1/3 because 4 > 3. The fraction wall makes the visual proof undeniable.
Teacher Reference · Common Errors
Bug Report: Grade 2 Misconceptions
⚠ BUG 1 · UNIT 2
Subtraction direction error
42−17: writes 7−2=5 in ones → gets 35 instead of 25.
→ Estimate first. Show: must exchange a ten.
⚠ BUG 2 · UNIT 2
Regrouping as magic
"Carry the 1" with no understanding that 1 = a ten.
→ Never say "carry". Use "exchange 10 ones for 1 ten".
⚠ BUG 3 · UNIT 7
Bigger denominator = bigger fraction
Student thinks 1/4 > 1/3 because 4 > 3.
→ Fraction wall: shade 1/3 and 1/4. Which piece is bigger?
⚠ BUG 4 · UNIT 3
× = just fast addition
Can only compute 3×4 as 4+4+4 — no group structure.
→ Array rotation: 3×4 and 4×3 are the same array sideways.
Practice Round 1 · Unit 1 · Expanded Form
Factory Challenge: Expanded Form
Tap each number to reveal its expanded form.
532
= ?
709
= ?
286
= ?
910
= ?
Watch 709 — zero in tens place is the key misconception. Ask: "What goes in the tens column? What does that zero mean for expanded form?"
Practice Round 2 · Unit 3 · Tables Rapid Fire
2×, 5×, 10× — Rapid Fire
Tap each card to reveal the answer.
Practice Round 3 · Unit 5 · Duration Word Problem
Elapsed Time Problem
The Problem (Session 37)
A factory shift starts at 9:15 AM and ends at 11:45 AM. How long is the shift?
Count on step by step — tap each row to reveal
9:15 → 9:30 = ?15 mintap
9:30 → 10:00 = ?30 mintap
10:00 → 11:00 = ?60 mintap
11:00 → 11:45 = ?45 mintap
Total = ?150 min = 2 hr 30 min ✓tap
Strategy: count from start time to the nearest round hour, then continue in chunks. Never subtract times directly — always count forward on the number line.
Practice Round 4 · Estimation Catch
Spot the Factory Error
Use estimation to find which answer is impossible. Tap to check.
234 + 189 = ?
423
Tap to check
147 + 253 = ?
310
Tap to check
6 × 5 = ?
30
Tap to check
482 − 136 = ?
346
Tap to check
147+253 — estimate is 150+250=400. Answer shown is 310 — difference of 90. Estimation caught it!
Grade 2 Mastery Checklist · 52 Sessions
Factory Quality Check
Decompose any 3-digit number H, T, O
Add & subtract 3-digit with regrouping
Estimate before every calculation
Recall 2×, 5×, 10× tables instantly
Solve division by sharing and grouping
Measure in m/cm, kg/g, L/mL
Read time to 5-minute intervals
Create & interpret tally/pictograph
Describe 2D shapes by properties
Compare unit fractions with reasoning
These are mastery gates. Any unchecked item means we work on it before Grade 3 content — regardless of school pace.
Preview · What Unlocks in Grade 3
Master Grade 2 — These Machines Unlock
✕
Full Times Tables
All tables to 10×10 — mastery, not memorisation
÷
Division with Remainders
What happens when sharing isn't perfectly equal
⅔
Equivalent Fractions
Why 1/2 = 2/4 = 3/6 — visual proof
📐
Perimeter & Area
Measure the world in two different ways
⚙
⚙
Session Complete
FACTORY CERTIFIED!
⭐⭐⭐⭐⭐
7 units · 52 sessions · Every concept built from concrete to abstract. EdTution Grade 2 Mathematics — CBSE · ICSE · IB · State Boards.